Discriminative feature extraction based on sparse and low-rank representation

The corrugated layer structure bismuth has been successfully tailored into negative thermal expansion along c axis by size effect. Pair distribution function and extended X-ray absorption fine structure are combined to reveal the local structural distortion for nanosized bismuth. The comprehensive method to identify the local structure of nanomaterials can benefit the regulating and controlling of thermal expansion in nanodivices.

Feature extraction (FE) methods based on low-rank representation (LRR) have become important topics in hyperspectral images (HSIs) data analysis. In this paper, a supervised FE method for HSIs data based on LRR with the ability to preserve the local pairwise constraints information (LRLPC) is proposed. LRLPC does not change the data dimensionality and only employs a technique to enrich the original feature space (OFS) and to obtain enriched feature space, which results in features richer than OFS. To overcome the problem of LRR in lacking the local structure information (LSI) of data, a local discriminative regularization term is imposed on the fitness function of LRR to keep the LSI of data. For nonlinear structure of data, LRLPC is extended to kernel LRLPC (KLRLPC) using kernel trick. Utilization of existing information in the pairwise constraints is useful for limited labeled samples situations as a common problem in HSI data analysis. The obtained experimental results using two well-known HSI data sets confirm the effectiveness of LRLPC and KLRLPC for dimension reduction and classification of HSIs.

BackgroundIdentifying different types of cancer based on gene expression data has become hotspot in bioinformatics research. Clustering cancer gene expression data from multiple cancers to their own class is a significance solution. However, the characteristics of high-dimensional and small samples of gene expression data and the noise of the data make data mining and research difficult. Although there are many effective and feasible methods to deal with this problem, the possibility remains that these methods are flawed.ResultsIn this paper, we propose the graph regularized low-rank representation under symmetric and sparse constraints (sgLRR) method in which we introduce graph regularization based on manifold learning and symmetric sparse constraints into the traditional low-rank representation (LRR). For the sgLRR method, by means of symmetric constraint and sparse constraint, the effect of raw data noise on low-rank representation is alleviated. Further, sgLRR method preserves the important intrinsic local geometrical structures of the raw data by introducing graph regularization. We apply this method to cluster multi-cancer samples based on gene expression data, which improves the clustering quality. First, the gene expression data are decomposed by sgLRR method. And, a lowest rank representation matrix is obtained, which is symmetric and sparse. Then, an affinity matrix is constructed to perform the multi-cancer sample clustering by using a spectral clustering algorithm, i.e., normalized cuts (Ncuts). Finally, the multi-cancer samples clustering is completed.ConclusionsA series of comparative experiments demonstrate that the sgLRR method based on low rank representation has a great advantage and remarkable performance in the clustering of multi-cancer samples.

BackgroundIn recent years protein structure prediction methods using local structure information have shown promising improvements. The quality of new fold predictions has risen significantly and in fold recognition incorporation of local structure predictions led to improvements in the accuracy of results.We developed a local structure prediction method to be integrated into either fold recognition or new fold prediction methods. For each local sequence window of a protein sequence the method predicts probability estimates for the sequence to attain particular local structures from a set of predefined local structure candidates.The first step is to define a set of local structure representatives based on clustering recurrent local structures. In the second step a discriminative model is trained to predict the local structure representative given local sequence information.ResultsThe step of clustering local structures yields an average RMSD quantization error of 1.19 Å for 27 structural representatives (for a fragment length of 7 residues). In the prediction step the area under the ROC curve for detection of the 27 classes ranges from 0.68 to 0.88.ConclusionThe described method yields probability estimates for local protein structure candidates, giving signals for all kinds of local structure. These local structure predictions can be incorporated either into fold recognition algorithms to improve alignment quality and the overall prediction accuracy or into new fold prediction methods.

Recently, low-rank and sparse model-based dimensionality reduction (DR) methods have aroused lots of interest. In this paper, we propose an effective supervised DR technique named block-diagonal constrained low-rank and sparse-based embedding (BLSE). BLSE has two steps, i.e., block-diagonal constrained low-rank and sparse representation (BLSR) and block-diagonal constrained low-rank and sparse graph embedding (BLSGE). Firstly, the BLSR model is developed to reveal the intrinsic intra-class and inter-class adjacent relationships as well as the local neighborhood relations and global structure of data. Particularly, there are mainly three items considered in BLSR. First, a sparse constraint is required to discover the local data structure. Second, a low-rank criterion is incorporated to capture the global structure in data. Third, a block-diagonal regularization is imposed on the representation to promote discrimination between different classes. Based on BLSR, informative and discriminative intra-class and inter-class graphs are constructed. With the graphs, BLSGE seeks a low-dimensional embedding subspace by simultaneously minimizing the intra-class scatter and maximizing the inter-class scatter. Experiments on public benchmark face and object image datasets demonstrate the effectiveness of the proposed approach.

Anchor-based multi-view graph clustering (AMVGC) has received abundant attention owing to its high efficiency and the capability to capture complementary structural information across multiple views. Intuitively, a high-quality anchor graph plays an essential role in the success of AMVGC. However, the existing AMVGC methods only consider single-structure information, i.e., local or global structure, which provides insufficient information for the learning task. To be specific, the over-scattered global structure leads to learned anchors failing to depict the cluster partition well. In contrast, the local structure with an improper similarity measure results in potentially inaccurate anchor assignment, ultimately leading to sub-optimal clustering performance. To tackle the issue, we propose a novel anchor-based multi-view graph clustering framework termed Efficient Multi-View Graph Clustering with Local and Global Structure Preservation (EMVGC-LG). Specifically, a unified framework with a theoretical guarantee is designed to capture local and global information. Besides, EMVGC-LG jointly optimizes anchor construction and graph learning to enhance the clustering quality. In addition, EMVGC-LG inherits the linear complexity of existing AMVGC methods respecting the sample number, which is time-economical and scales well with the data size. Extensive experiments demonstrate the effectiveness and efficiency of our proposed method.

In this paper, we propose a novel single image super-resolution (SR) method based on low-rank sparse representation with self-similarity learning. Sparse representation is known as a promising method for SR. However, the sparse codes for low resolution (LR) patches gained by conventional method are not faithful to those for the original high resolution (HR) ones. To overcome this defect, we explore the structures of sparse representation for nonlocal similar patches in natural images by low-rank strategy. It assumes that the sparse codes for nonlocal similar patches should be low-rank. By low-rank constraint, similar components of sparse codes are shared and coding noises are removed, which improves coding accuracy and SR performance. Furthermore, we utilize self-similarity learning framework to generate a self-examples dictionary compatible to the low-rank sparse representation based SR. Experimental results demonstrate that our proposed method can recover good SR results both quantitatively and perceptually.

As an emerging paradigm, Mobile CrowdSensing (MCS) network based fingerprint positioning technology can implement the site survey cheap and fast, and provide a more reliable location-based service for users. However, limited by the differences among individuals, the fingerprints collected from MCS network are troubled by fingerprint ineffectiveness or element missing problems. In order to ensure the availability of fingerprints, in this paper we propose a novel Low-rank and Sparse representation based Tensor Completion (LSTC) fingerprint recovery method to recover the ineffective fingerprints and the missing fingerprint elements accurately in MCS network. Specifically, the tensor low-rank characterization is used to exploit the global structure of the location fingerprints, and the tensor sparsity characterization is used to exploit the local structure of the location fingerprint elements. To promote the global optimal solution solving rapidly, a weight compensation scheme is proposed to fill the convex relaxation gap caused by the approximation of low-rank and sparsity. Meanwhile, to represent the local sparse characterization effectively, orthogonal dictionary learning is introduced and integrated into LSTC. The experimental results show that by using the tensor global and local structure information properly, the proposed LSTC can recover the fingerprint effectively, without jeopardizing the positioning accuracy.

Dimensionality reduction is an essential task in hyperspectral image processing. How to preserve the original intrinsic structure information and enhance the discriminant ability is still a challenge in this area. Recently, with the advantage of preserving global intrinsic structure information, low-rank representation has been applied to dimensionality reduction and achieved promising performance. By exploiting the submanifold information of the original data set, multimanifold learning is effective in enhancing the discriminant ability of the processed data set. In addition, due to the ability of preserving the spatial neighborhood structure information, the tensor analysis has become a popular technique for hyperspectral image processing. Motivated by the above-mentioned analysis, a novel tensor-based low-rank graph with multimanifold regularization (T-LGMR) for dimensionality reduction of hyperspectral images is proposed in this paper. In the T-LGMR, a low-rank constraint is employed to preserve the global data structure while multimanifold information is utilized to enhance the discriminant ability, and tensor representation is used to preserve the spatial neighborhood information. Finally, dimensionality reduction is achieved in the graph embedding framework. Experimental results on three real hyperspectral data sets demonstrate the superiority of the proposed method over several state-of-the-art approaches.

Low-rank representation with local constraint for graph construction

Anomaly detection (AD) aims to distinguish the data points that are inconsistent with the overall pattern of the data. Recently, unsupervised anomaly detection methods have aroused huge attention. Among these methods, feature representation (FR) plays an important role, which can directly affect the performance of anomaly detection. Sparse representation (SR) can be regarded as one of matrix factorization (MF) methods, which is a powerful tool for FR. However, there are some limitations in the original SR. On the one hand, it just learns the shallow feature representations, which leads to the poor performance for anomaly detection. On the other hand, the local geometry structure information of data is ignored. To address these shortcomings, a graph regularized deep sparse representation (GRDSR) approach is proposed for unsupervised anomaly detection in this work. In GRDSR, a deep representation framework is first designed by extending the single layer MF to a multilayer MF for extracting hierarchical structure from the original data. Next, a graph regularization term is introduced to capture the intrinsic local geometric structure information of the original data during the process of FR, making the deep features preserve the neighborhood relationship well. Then, a L1-norm-based sparsity constraint is added to enhance the discriminant ability of the deep features. Finally, a reconstruction error is applied to distinguish anomalies. In order to demonstrate the effectiveness of the proposed approach, we conduct extensive experiments on ten datasets. Compared with the state-of-the-art methods, the proposed approach can achieve the best performance.

Feature extraction methods in the industrial process may affect the performance of process monitoring and fault assessment. In order to reduce the influence of model preference, a novel fault assessment method integrating global and local structure information is proposed by using the strategy of parallel extraction and weighted combination. First, kernel sparse locally linear embedding and kernel principal component analysis models are constructed to handle nonlinear system states and describe the local and global information in parallel. Second, the fault assessment indicators are obtained through support vector data description models. Then, a comprehensive fault assessment index is established by the weighted fusion method, which can keep the global and local neighbor information of the original sample space, and thus more feature information is included. Finally, the feasibility and effectiveness of the proposed assessment method are illustrated by the application in the simulation process of Tennessee Eastman Process, and the results show that the fusion of two basic models can bring a model with better generalization performance than a single model.

Principal Component Analysis Network (PCANet) is a feature learning algorithm which is widely used in face recognition and object classification. However, original PCANet still has some shortages. One is that PCA algorithm only extracts features by considering the global structure. The other lies in that the original PCANet only employs one particular single layer convolutional results, which loses the information of other convolutional layers. In this paper, we propose a new simple and efficient convolutional neural network called global and local structure network (GLSNet) to address the problems. The network extracts the features both from the global structure and the local structure of the original data space. Specifically, a principal component analysis (PCA) convolutional layer which learns the filters by PCA algorithm is used to remove the noises and redundant information at the first stage. Then at the second stage, another PCA convolution is added to extract features by considering the global structure. As for the local structure, we use the neighborhood preserving embedding (NPE) algorithm to learn the convolutional filters. At the output stage, the global structure feature extracted by PCA convolution and the local structure feature extracted by NPE convolution is concatenated as a united feature. Furthermore, the first layer convolutional feature is also taken into consideration to obtain shallow-level information. Finally, these features are concatenated as a united feature, and a spatial pyramid pooling layer is followed to pool above the united features. To test the effectiveness of the proposed algorithm, the experiments on some image datasets, including three types: human face dataset, object dataset, and handprinted dataset, proceeded. And it performs better than the original PCANet and some improvement algorithms of PCANet, such as PLDANet, and MMPCANet.

The diesel engine fault data is nonlinear and it’s difficult to extract the characteristic information. Kernel Principal Component Analysis (KPCA) is used to extract features of nonlinear data, only considering global structure. Kernel Locality Preserving Projection (KLPP) considers the local feature structure. So an improved algorithm for global and local structure preserving is proposed to extract the feature of data. The improved feature extraction algorithm combining KPCA and KLPP, avoids the loss of information considering the global and local feature structure and then uses the modified K-NN algorithm for fault classification. In this paper, the software AVL BOOST is used to simulate the faults of diesel engine. The simulation experiments indicate the proposed method can extract the feature vectors effectively, and shows good classification performance.

Subspace learning and reconstruction have been widely explored in recent transfer learning work and generally a specially designed projection and reconstruction transfer matrix are wanted. However, existing subspace reconstruction based algorithms neglect the class prior such that the learned transfer function is biased, especially when data scarcity of some class is encountered. Different from those previous methods, in this paper, we propose a novel reconstruction-based transfer learning method called Class-specific Reconstruction Transfer Learning (CRTL), which optimizes a well-designed transfer loss function without class bias. Using a class-specific reconstruction matrix to align the source domain with the target domain which provides help for classification with class prior modeling. Furthermore, to keep the intrinsic relationship between data and labels after feature augmentation, a projected Hilbert-Schmidt Independence Criterion (pHSIC), that measures the dependency between two sets, is first proposed by mapping the data from original space to RKHS in transfer learning. In addition, combining low-rank and sparse constraints on the class-specific reconstruction coefficient matrix, the global and local data structures can be effectively preserved. Extensive experiments demonstrate that the proposed method outperforms conventional representation-based domain adaptation methods.